What is the "white stuff" that seems to trail high flying planes ?

As we go higher up in the atmosphere (at about 8 km, temp is approx. -40c), both 

pressure and temperature fall. The engines of the airplanes are venting exhaust 

containing water vapor, carbon dioxide (CO2), small amounts of nitrogen oxides (NO), 

hydrocarbons, carbon monoxide, sulfur gases, soot and metal particles at a much higher

pressure and temperature. It is a well-known fact that cool air has lesser capacity to 

hold moisture than hot air. Hence, the water vapor (some from the airplane, some already 

present in the atmosphere) is quickly cooled and condenses and freezes on the surface 

provided by the carbon dioxide, soot and metal particles forming a cloud behind the airplane.

Such clouds are called "contrails". How long a contrail remains intact, depends on the 

humidity structure and winds of the upper troposphere. If the atmosphere is near saturation, 

the contrail may exist for sometime. On the other hand, if the atmosphere is dry then as the 

contrail mixes with the environment, it dissipates.

You can verify how contrails form by observing the following fact:

On a cold winter's day you can see your breath.